Probability worksheet — GCSE Foundation

1.A café offers 3 types of sandwich, cheese, ham and egg, and 4 types of drink, tea, coffee, juice and water. A customer chooses one sandwich and one drink at random. Work out the probability that the customer chooses egg and water.

2.A card is taken at random from an ordinary pack of 52 playing cards. The probability that the card is a diamond is 1/4. Work out the probability that the card is not a diamond.

3.The probability that Priya scores with a netball shot is 3/4. She takes two shots, and the shots are independent. Work out the probability that she scores with her first shot but misses her second shot.

4.A library recorded loans for 250 books over a week, using a frequency tree. The first branch splits the books into 160 fiction and 90 non-fiction. Of the fiction books, 112 were returned on time and the rest were returned late. All the non-fiction books were returned on time. Work out the probability that a book, chosen at random from the 250, was returned late. Give your answer as a fraction in its simplest form.

5.At a quiz night, each team's result is a win, a draw or a loss, and no team can have more than one of these results. The probability that a team wins is 42% and the probability that a team draws is 18.5%. Work out the probability, as a percentage, that a team does not win and does not draw.

6.A fair spinner has 8 equal sections. 3 of the sections are red. The spinner is spun 240 times. Work out how many times you would expect it to land on red.

7.The universal set is {1, 2, 3, ..., 30}. Set A is the set of multiples of 4 between 1 and 30. Work out n(A′), the number of elements not in A.

8.At a fun run, a raffle stall charges £1.50 per ticket. The probability that any one ticket wins a prize worth £8 is 0.12, and a losing ticket wins nothing. Nadia buys 25 tickets. Work out how much money Nadia should expect to lose in total.

9.Priya and Ben each want to estimate the probability that a coin lands on heads. Priya flips the coin 50 times and works out her relative frequency. Ben flips the same coin 500 times and works out his relative frequency. Whose relative frequency is more likely to be close to the true probability? Give a reason for your answer.

10.In a board game Mia moves forward by the total of two ordinary fair dice. Work out the probability that her total is 7. Give your answer as a fraction in its simplest form.

11.A jar contains counters that are pink, gold or grey only. The probability that a counter taken at random is pink is 0.2 and the probability that it is gold is 0.45. The jar contains 60 counters in total. Work out the number of grey counters.

12.A bag contains 20 counters. 8 of the counters are red and 12 are blue. A counter is taken at random, its colour is recorded, and it is put back in the bag. This is done 150 times. Work out how many red counters you would expect to be recorded.

13.A biased spinner is spun 200 times. It lands on red 70 times, on blue 50 times, and on green 80 times. Using these results, work out the expected number of times the spinner does NOT land on red, in 500 spins of the same spinner.

14.A padlock code is formed by arranging three different digits chosen from 2, 3, 4 and 5, with no digit repeated. Work out how many different three-digit codes can be made.

15.The probability that Isla answers a quiz question correctly is 0.8. She answers three questions, and her answers are independent of each other. Work out the probability that she answers all three correctly.